demorotreflect.m

这是几何代数的matlab工具包

     disp('>> % |');
     % |
     disp('>> % |  TWO REFLECTIONS MAKE A ROTATION');
     % |  TWO REFLECTIONS MAKE A ROTATION
     disp('>> % |');
     % |
     v = e1; %/
     w = e2; %/
     I2 = v^w/norm(v^w); %/
     phi = pi/4;%/
     R = gexp(-I2*phi/2);%/
     x = e1+e3;%/
     clf;%/
     draw(x,'r'); GAtext(1.1*x,'x','r'); %/
     axis off; %/
     draw(I2,'y'); %/
     draw(v,'g'); GAtext(1.1*v,'v','g'); %/
     Rv = R*v; %/
     draw(Rv,'g'); GAtext(1.1*Rv,'w','g'); %/
     disp('>> axis([-0.6 1 -0.6 0.7 -1 1]);');
     axis([-0.6 1 -0.6 0.7 -1 1]);
     disp('>> % |  a vector x and the v^w- plane ');
     % |  a vector x and the v^w- plane 
     disp('>> % |');
     % |
     GAprompt; %/
     Sx = v*x/v; %/
     draw(Sx,'b'); GAtext(1.1*Sx,'v x v^{-1}','b'); %/
     DrawPolyline({x,Sx},'m'); %/
     disp('>> axis([-0.6 1 -0.6 0.7 -1 1]);');
     axis([-0.6 1 -0.6 0.7 -1 1]);
     disp('>> % |  first reflection, in v');
     % |  first reflection, in v
     disp('>> % |');
     % |
     GAprompt; %/
     Rx = Rv*Sx/Rv; %/
     draw(Rx,'r'); GAtext(1.1*Rx,'(w v) x (w v)^{-1}','r'); %/
     DrawPolyline({Sx,Rx},'m'); %/
     disp('>> axis([-0.6 1 -0.6 0.7 -1 1]);');
     axis([-0.6 1 -0.6 0.7 -1 1]);
     disp('>> % |  second reflection, in v');
     % |  second reflection, in v
     disp('>> % |');
     % |
        n = 10; %% number of points on rotation arc %/
     GAprompt;
        DR = gexp(-I2*phi/2/n); %/
        y = x; %/
        for i=1:n %/
           yy = DR*y/DR; %/
           DrawPolyline({y,yy},'k'); %/
           y = yy; %/
        end %/
     rej = (x^I2)/I2; %/ 
     DrawPolyline({x,rej,Rx},'k'); %/
     DrawPolyline({0.00001*e1,rej},'k'); %/
     disp('>> axis([-0.6 1 -0.6 0.7 -1 1]);');
     axis([-0.6 1 -0.6 0.7 -1 1]);
     disp('>> % |  the result is a rotation in the v^w-plane,');
     % |  the result is a rotation in the v^w-plane,
     disp('>> % |  over twice the angle from v to w');
     % |  over twice the angle from v to w
     disp('>> % |');
     % |
     GAorbiter(-360,10); %/